Two different answers, depending on whether you mean the filament or the finished part.
As a solid polymer: polypropylene, at 0.89 to 0.92 g/cm³. It is the only common filament that floats, and a kilogram of it holds 1,111.11 cm³ — 461.95 m of 1.75 mm stock, more length per kilogram than anything else here.
As a printed part: LW-PLA, which is stored at 0.4 to 1.24 g/cm³ and can reach the bottom of that range.
LW-PLA is a different kind of answer
The wide band is not a manufacturing tolerance. LW-PLA contains a foaming agent that expands when the plastic is run hot, so the density of the finished part is something you choose by setting temperature and flow.
Print it cool and it behaves like ordinary PLA at 1.24 g/cm³. Print it hot with the flow turned down to compensate for expansion and the same spool produces parts at a fraction of the mass. That is why it dominates radio-controlled aircraft and any application where grams matter more than surface finish.
The trade is a rough, matte, slightly furry surface and a process window that takes calibration to find.
Why polypropylene is rarely the answer anyway
It is rated difficulty 5, contracts 1 to 2.5% — the worst warping on this site outside nylon — requires an enclosure, and almost nothing sticks to it, including the bed and any adhesive you might use afterwards.
People choose PP for its chemical resistance and its living hinges, not for its weight.
The practical lightweight choices
For a part that has to be light and printable, the realistic options are ordinary PLA with fewer walls and less infill, or LW-PLA if you are prepared to calibrate it. Geometry usually beats material here — a well-designed part at 10% infill and two walls is lighter than a badly-designed one in an exotic polymer.
Foamed and filled grades break this ranking entirely, since both change the density without changing the polymer — start from the per-material density table and put whatever figure your own spool declares into the length and weight converter.